The Formation of High Mass Stars Richard I. Klein UC Berkeley, Department of Astronomy and Lawrence Livermore National Laboratory Collaborators Mark Krumholz (Princeton University) and Chris McKee (UC Berkeley) This work was performed under the auspices of the U.S. Department of Energy by the University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. UCRL-PRES Zurich September 17, 2007 Next Generation of Computational Models

UCRL-PRES Outstanding Challenges of Massive Star Formation What is the formation Mechanism: Gravitational collapse of an unstable turbulent cloud; Competitive Bondi-Hoyle accretion; Collisional Coalescence? How can gravitationally collapsing clouds overcome the Eddington limit due to radiation pressure? What determines the upper limit for High Mass Stars? (120M sun  150M sun ) How do feedback mechanisms such as protostellar outflows and radiation affect protostellar evolution? These mechanisms can also have a dramatic effect on cluster formation How do the systems in which massive stars are present form?

UCRL-PRES Theoretical Challenges of High Mass Star Formation 1. Effects of Strong Radiation Pressure —Massive stars M  20 M  have t K < t form (Shu et al. 1987) and begin nuclear burning during accretion phase  Radiates enormous energy  For M  100 M  however  dust >>  T  But, observations show M ~ 100 M  (Massey 1998, 2003) Fundamental Problem: How is it possible to sustain a sufficiently high-mass accretion rate onto protostellar core despite “Eddington” barrier? Does radiation pressure provide a natural limit to the formation of high mass stars?

UCRL-PRES Theoretical Challenges of High Mass Star Formation (cont.) 2. Effects of Protostellar outflows —Massive stars produce strong radiation driven stellar winds with momentum fluxes —Massive YSO have observed (CO) protostellar outflows where (Richer et al. 2000; Cesaroni 2004)  If outflows where spherically symmetric this would create a greater obstacle to massive star formation than radiation pressure but, flows are found to be collimated with collimation factors 2-10 (Beuther 2002, 2003, 2004) Fundamental Problem: How do outflows effect the formation of Massive stars? Do outflows limit the mass of a star?

UCRL-PRES Physical Effects in High-Mass Star Formation Photoionization: —Effects quenched for moderate accretion rates ~10 -4 M  /yr for spherically symmetric infall —In disk accretion, material above and below disk confine ionized region close to stellar surface —Outflows are sufficient to quench ionization (Tan and McKee 2003)  Omit Photoionization as a first approximation Magnetic fields —Gravity dominates magnetic fields when M > M B  B 3 /n 2 so magnetic fields are dynamically unimportant for high mass cores (Shu et al. 1987) —At high densities B  n 1/2 so M B  n -1/2 and since n  10 6 in massive star forming regions, M B is substantially reduced —Observations of magnetic fields in high mass cores inconlcusive  Neglect of magnetic fields is a reasonable first approximation

UCRL-PRES Physical Effects in High-Mass Star Formation (cont.) Dust —Critical role in massive star formation  couples gas to radiation flux from central star  need radiation transport and multi-species models with good microphysics Photostellar outflows —Molecular outflows in neighborhood of massive stars ~ M  /yr. Force required to drive such outflows F co > 10 – 100 L BOL /c  Outflows may be important to protostellar evolution Three-Dimensional Effects —Interaction of radiation with infalling envelope subject to radiation driven instabilities —Interaction of protostellar outflow with infalling envelope possibly unstable —Accretion disks develop non-axisymmetric structures in turbulent flows  Three dimensional simulations are crucial

UCRL-PRES Equations of Gravito-Radiation Hydrodynamics to order v/c ( Krumholz, Klein & McKee 2007a) (Continuity) (Gas momentum) (Gas energy) (Poisson) (Radiation energy) (Flux-limited diffusion approximation) Equations exact to (v/c) in static diffusion regime.

UCRL-PRES High Mass Star Formation Simulation Physics Euler equations of compressible gas dynamics with gravity Radiative transfer and radiation pressure in the gray, flux-limited diffusion approximation  radiative feedback Model of dust opacity based on Pollack et al. (1994) (6 species) Outflows: hydromagnetic outflow models  Dynamical Feedback Eulerian sink particles: —Created when the density in a cell exceeds the local Jeans density (Krumholz, McKee, & Klein 2004) —Free to move through the grid and continue to accrete gas —Sink particles feed radiation and (for some runs) winds back into the grid based on a protostellar model —Model includes accretion, KH contraction, deuterium and hydrogen burning (McKee & Tan 2003), x-winds Capability to handle the enormous range of scales involved  AMR

UCRL-PRES Physics Implementation Our AMR code is a combination of C++ and FORTRAN 90  Uses parallel MPI-based Box Lib Library ORION is our magneto-radiation-hydrodynamics AMR code We Solve: Parallel, 3-D coupled self-gravitating-Radiation-Hydrodynamics on Adaptive Meshes  Multi-Scale Physics I. Hydrodynamics: is solved with conservative, high order, time explicit Godunov scheme with Approximate Riemann Solver  Multi-fluid Hydrodynamics II. Self-Gravity: We employ parallel, scalable, multi-grid solution algorithms  We use implicit multi-grid iteration to first solve Poisson Equation on a single level

UCRL-PRES Physics Implementation (cont.)  Level solutions are then coupled and iterated to convergence to obtain solution for gravitational potential on all levels III. Radiation Transfer: Non-Equilibrium Flux-Limited diffusion including important O(v/c) terms - Radiation solved implicity with parallel multi-grid, iteration scheme taking into account multi-level solves  Solutions must be obtained which couple all grids at a single refinement level, or even across multiple level IV. Ideal MHD: fully 2nd order unsplit Godunov MHD  We are now implementing this in our AMR self-gravity rad-hydro code  Much better dissipation properties than split staggered mesh schemes (Crockett, Collella, Fisher, Klein & McKee JCP 2004)

UCRL-PRES HMSF Initial Conditions: Non-Turbulent r –3/2 density profile, r = 0.1–0.2 pc, M = 100–200 M sun, slow solid-body rotation:  = 0.02, dynamic range = 8192

UCRL-PRES Non-Turbulent IC: Early Evolution At early stages the star accretes steadily and a Keplerian disk forms. Cylindrical symmetry is maintained.

UCRL-PRES Non-Turbulent IC: Radiation Bubble Formation At higher luminosities, radiation pressure forms bubbles above and below the accretion disk. Bubble growth is up-down and cylindrically asymmetric.

UCRL-PRES Continued Expansion of Radiation Bubble

UCRL-PRES High Mass Disk and Formation of Expanding Radiation Driven Bubble

UCRL-PRES Rayleigh-Taylor Instability in Radiation Driven Bubble

UCRL-PRES Collapse of radiation driven bubble

UCRL-PRES HMSF: Turbulent Initial Conditions r –3/2 density profile, Gaussian random velocity field with power on large scales, kinetic energy ~ potential energy  Mach number ~8.5, dynamic range = 16,348

UCRL-PRES HMSF Protostellar Evolution Turbulent ICs Non Turbulent ICs

UCRL-PRES Radius, Accretion Rate and Luminosity of Primary Star start of Deuterium burning accretion luminosity Principal source of raising temperature in the core is accretion luminosity which is the dominant source of energy prior to nuclear burning

UCRL-PRES Temperature Distribution in 100 Solar Mass Core T>100 K, BART>300 K, BAR T>300 K, RT T>100 K, RT T>50 K, RTALL T>50 K, BAR Accretion luminosity transported by radiation heats a radius of 1000 AU of the core to > 50K and substantial parts of the core to > 100K

UCRL-PRES Evolution of 100 Solar Mass Turbulent Protostellar Core Radiative heating results in the formation of a primary high mass star and 2 low mass stars in the disk

UCRL-PRES Evolution of 100 Solar Mass Turbulent Isothermal Protostellar Core Isothermal or barotropic models result in the formation of a multitude of low mass stars only  erroneous fragmentation

UCRL-PRES Observing Massive Disks with ALMA Integrated T B in simulated 1000 s / pointing ALMA observation of disk at 0.5 kpc in CH 3 CN GHz (KKM 2007c, ApJ,)

UCRL-PRES Effects of Protostellar Outflows High mass protostars have outflows that look like larger versions of low mass protostellar outflows (Beuther et al. 2004) Outflows are launched inside star’s dust destruction radius Due to high outflow velocities, there is no time for dust grains to regrow inside outflow cavities. Grains reach only ~10 –3  m by the time they escape the core. Because grains are small, outflow cavities are optically thin. Thin cavities can be very effective at collimating protostellar radiation, reducing the radiation pressure force in the equatorial plane Krumholz, McKee & Klein, (2005) using toy Monte-Carlo radiative transfer calculations find outflows cause a factor of 5 – 10 radiation pressure force reduction Outflows may be responsible for driving turbulence in clumps (Li & Nakamura 2006) 

UCRL-PRES Protostellar Outflows in High-Mass Star Formation Temperature DistributionRadiation and Gravitational Forces Temperature distribution from Monte Carlo diffusion (Whitney, et. al. 2003); Radiation transfer with ray solution to get radiative forces Envelope rotationally flattened density dist.; cavity shape Z=a  b ; M=50M  ZAMS; 50M  envelope With no wind cavity; f rad > f grav everywhere except inside the accretion disk  accretion halted With wind cavity, f rad < f grav outside disk radius  accretion can continue

UCRL-PRES HMSF with Outflows: Very Early 3-D Evolution Early results show that radiation is collimated effectively by outflow cavities: radiation energy density is factor of ~5 higher inside cavity

UCRL-PRES Advances Necessary in Algorithmic Performance and Scalability for High Mass Star Formation State-of-the-art simulations follow collapse from the scale of turbulent cores to stars (KKM 2007) Dynamic range > 10 4 Simulations will require more realistic initial conditions in core derived from the outer scale imposed by turbulent clumps (M ~ several X 10 3 M  ) Simulations are just beginning to follow collapse from turbulent Clumps  Cores  Stars with radiative feedback and AMR Dynamic Range > 10 5 Current state-of-the-art (Krumholz, Klein & McKee 2006, 07) require months to evolve high mass stars on parallel machines (~ 256 processors) with Grey Radiation Transfer  multi-frequency will be several times more expensive Future simulations will evolve GMCs  Clumps  Cores  Stars Dynamic Range > For galaxy simulations to incorporate star formation Galaxy  GMCs  Clumps  Cores  Stars Dynamic Range > 3x x10 10

UCRL-PRES Summary and Future Directions 3-D high resolution AMR simulations with ORION achieves protostellar masses considerably above previous 2-D axisymmetric gray simulations Two new mechanisms have been shown to overcome radiation pressure barrier to achieve high mass star formation —3-D Rayleigh-Taylor instabilities in radiation driven bubbles appear to be important in allowing accretion onto protostellar core —Protostellar outflows resulting in optically thin cavities promote focusing of radiation and reduction of radiation pressure  enhances accretion —Radiation feedback from accreting protostars inhibits fragmentation ALMA observations will help distinguish between competing models of high mass star formation  gravitational core collapse predicts large scale disks Future Directions Multi-frequency radiation-hydrodynamics and inclusion of ionization Improvement in flux limited diffusion (Monte-Carlo; Sn transport; Variable Edd Tensor) Improvement in dust physics (e.g. shattering; coagulation; multi-species) Evolution of wind outflow models and interaction with infalling envelope Self consistent evolution of high mass turbulent cores from large scale turbulent clump Inclusion of MHD  can launch hydromagnetic wind; possible photon bubble instab. 

UCRL-PRES Back up Slides

UCRL-PRES Radiation Transport Results in Suppression of Large Scale Fragmentation in Massive Star Formation 0.26 pc 6700 AU Most of the available mass in turbulent cloud goes into one massive star.

UCRL-PRES High Mass Disk at 27,000 yr. (Krumholz, Klein & McKee 2007b) 0.6 pc radiusDisk radius 3000 AU

UCRL-PRES Observing Massive Disks Integrated T B in simulated 1000 s / pointing ALMA observation of disk at 0.5 kpc in CH 3 CN GHz (KKM 2007c, ApJ, in press)

UCRL-PRES Adaptive Mesh Overview A block-structured refinement strategy combines the advantages of adaptive mesh refinement with the efficiencies provided by uniform grids For hyperbolic systems, such as the advection component of fluid dynamics, explicit difference schemes can be used which minimize communication —A serial algorithm can proceed one grid at a time —A parallel algorithm can process many grids at once. Library support for this approach is provided by CCSE at LBL. For parabolic and elliptic systems, such as those associated with radiation diffusion, implicit difference schemes must be used. Solutions must be obtained which couple all grids at a single refinement level, or even across multiple levels. —Interactive solvers based on multigrid provide efficient solutions. —We use the hypre parallel multigrid library developed in CASC for this part of the algorithm